4.4 Mesh generation with the snappyHexMesh utility

[prev] [next]

This section describes the mesh generation utility, snappyHexMesh , supplied with OpenFOAM. The snappyHexMesh utility generates 3-dimensional meshes containing hexahedra (hex) and split-hexahedra (split-hex) automatically from triangulated surface geometries in Stereolithography (STL) format. The mesh approximately conforms to the surface by iteratively refining a starting mesh and morphing the resulting split-hex mesh to the surface. An optional phase will shrink back the resulting mesh and insert cell layers. The specification of mesh refinement level is very flexible and the surface handling is robust with a pre-specified final mesh quality. It runs in parallel with a load balancing step every iteration.

$\relax \special {t4ht=$

Figure 4.8: Schematic 2D meshing problem for snappyHexMesh

4.4.1 The mesh generation process of snappyHexMesh

The process of generating a mesh using snappyHexMesh will be described using the schematic in Figure 4.8. The objective is to mesh a rectangular shaped region (shaded grey in the figure) surrounding an object described by and STL surface, e.g. typical for an external aerodynamics simulation. Note that the schematic is 2-dimensional to make it easier to understand, even though the snappyHexMesh is a 3D meshing tool.

In order to run snappyHexMesh, the user requires the following:

surface data files in STL format, either binary or ASCII, located in a constant/triSurface sub-directory of the case directory;
a background hex mesh which defines the extent of the computational domain and a base level mesh density; typically generated using blockMesh, discussed in section 4.4.2.
a snappyHexMeshDict dictionary, with appropriate entries, located in the system sub-directory of the case.

The snappyHexMeshDict dictionary includes: switches at the top level that control the various stages of the meshing process; and, individual sub-directories for each process. The entries are listed in Table 4.4.

Keyword	Description	Example

castellatedMesh	Create the castellated mesh?	true
snap	Do the surface snapping stage?	true
addLayers	Add surface layers?	true
mergeTolerance	Merge tolerance as fraction of bounding box of initial mesh	1e-06
debug	Controls writing of intermediate meshes and screen printing
	— Write final mesh only	0
	— Write intermediate meshes	1
	— Write volScalarField with cellLevel for post-processing	2
	— Write current intersections as .obj files	4
geometry	Sub-dictionary of all surface geometry used
castellatedMeshControls	Sub-dictionary of controls for castellated mesh
snapControls	Sub-dictionary of controls for surface snapping
addLayersControls	Sub-dictionary of controls for layer addition
meshQualityControls	Sub-dictionary of controls for mesh quality

Table 4.4: Keywords at the top level of snappyHexMeshDict.

A full list of analytical shapes can be found online at https://www.openfoam.com/documentation/cpp-guide/html/guide-meshing-snappyhexmesh-geometry.html

All the geometry used by snappyHexMesh is specified in a geometry sub-dictionary in the snappyHexMeshDict dictionary. The geometry can be specified through an STL surface or bounding geometry entities in OpenFOAM. An example is given below:

geometry
{
    sphere.stl // STL filename
    {
        type triSurfaceMesh;
        regions
        {
            secondSolid             // Named region in the STL file
            {
                name mySecondPatch; // User-defined patch name
            }                       // otherwise given sphere.stl_secondSolid
        }
    }

    box1x1x1  // User defined region name
    {
        type   searchableBox;       // region defined by bounding box
        min    (1.5 1 -0.5);
        max    (3.5 2 0.5);
    }

    sphere2  // User defined region name
    {
        type   searchableSphere;    // region defined by bounding sphere
        centre (1.5 1.5 1.5);
        radius 1.03;
    }
};

4.4.2 Creating the background hex mesh

Before snappyHexMesh is executed the user must create a background mesh of hexahedral cells that fills the entire region within by the external boundary as shown in Figure 4.9.

$\relax \special {t4ht=$

Figure 4.9: Initial mesh generation in snappyHexMesh meshing process

This can be done simply using blockMesh. The following criteria must be observed when creating the background mesh:

the mesh must consist purely of hexes;
the cell aspect ratio should be approximately 1, at least near surfaces at which the subsequent snapping procedure is applied, otherwise the convergence of the snapping procedure is slow, possibly to the point of failure;
there must be at least one intersection of a cell edge with the STL surface, i.e. a mesh of one cell will not work.

$\relax \special {t4ht=$

Figure 4.10: Cell splitting by feature edge in snappyHexMesh meshing process

4.4.3 Cell splitting at feature edges and surfaces

Cell splitting is performed according to the specification supplied by the user in the castellatedMeshControls sub-dictionary in the snappyHexMeshDict. The entries for castellatedMeshControls are presented in Table 4.5.

Keyword	Description	Example

locationInMesh	Location vector inside the region to be meshed	(5 0 0)
	N.B. vector must not coincide with a cell face either before or during refinement
maxLocalCells	Maximum number of cells per processor during refinement	1e+06
maxGlobalCells	Overall cell limit during refinement (i.e. before removal)	2e+06
minRefinementCells	If $≥ \relax \special {t4ht=$ number of cells to be refined, surface refinement stops	0
maxLoadUnbalance	Maximum processor imbalance during refinement where a value of $0 \relax \special {t4ht=$ represents a perfect balance	0.1
nCellsBetweenLevels	Number of buffer layers of cells between different levels of refinement	1
resolveFeatureAngle	Applies maximum level of refinement to cells that can see intersections whose angle exceeds this	30
allowFreeStandingZoneFaces	Allow the generation of free-standing zone faces	flase
features	List of features for refinement
refinementSurfaces	Dictionary of surfaces for refinement
refinementRegions	Dictionary of regions for refinement

Table 4.5: Keywords in the castellatedMeshControls sub-dictionary of snappyHexMeshDict.

The splitting process begins with cells being selected according to specified edge features first within the domain as illustrated in Figure 4.10. The features list in the castellatedMeshControls sub-dictionary permits dictionary entries containing a name of an edgeMesh file and the level of refinement, e.g.:

features
(
    {
        file "features.eMesh"; // file containing edge mesh
        level 2;               // level of refinement
    }
);

The edgeMesh containing the features can be extracted from the STL geometry file using surfaceFeatureExtract , e.g.

surfaceFeatureExtract -includedAngle 150 surface.stl features

Following feature refinement, cells are selected for splitting in the locality of specified surfaces as illustrated in Figure 4.11.

$\relax \special {t4ht=$

Figure 4.11: Cell splitting by surface in snappyHexMesh meshing process

The refinementSurfaces dictionary in castellatedMeshControls requires dictionary entries for each STL surface and a default level specification of the minimum and maximum refinement in the form (<min> <max>). The minimum level is applied generally across the surface; the maximum level is applied to cells that can see intersections that form an angle in excess of that specified by resolveFeatureAngle .

The refinement can optionally be overridden on one or more specific region of an STL surface. The region entries are collected in a regions sub-dictionary. The keyword for each region entry is the name of the region itself and the refinement level is contained within a further sub-dictionary. An example is given below:

refinementSurfaces
{
    sphere.stl
    {
        level (2 2); // default (min max) refinement for whole surface
        regions
        {
            secondSolid
            {
                level (3 3); // optional refinement for secondSolid region
            }
        }
    }
}

4.4.4 Cell removal

Once the feature and surface splitting is complete a process of cell removal begins. Cell removal requires one or more regions enclosed entirely by a bounding surface within the domain. The region in which cells are retained are simply identified by a location vector within that region, specified by the locationInMesh keyword in castellatedMeshControls. Cells are retained if, approximately speaking, 50% or more of their volume lies within the region. The remaining cells are removed accordingly as illustrated in Figure 4.12.

$\relax \special {t4ht=$

Figure 4.12: Cell removal in snappyHexMesh meshing process

$\relax \special {t4ht=$

Figure 4.13: Cell splitting by region in snappyHexMesh meshing process

4.4.5 Cell splitting in specified regions

Those cells that lie within one or more specified volume regions can be further split as illustrated in Figure 4.13 by a rectangular region shown by dark shading. The refinementRegions sub-dictionary in castellatedMeshControls contains entries for refinement of the volume regions specified in the geometry sub-dictionary. A refinement mode is applied to each region which can be:

inside refines inside the volume region;
outside refines outside the volume region
distance refines according to distance to the surface; and can accommodate different levels at multiple distances with the levels keyword.

For the refinementRegions , the refinement level is specified by the levels list of entries with the format(<distance> <level>). In the case of inside and outside refinement, the <distance> is not required so is ignored (but it must be specified). Examples are shown below:

refinementRegions
{
    box1x1x1
    {
        mode inside;
        levels ((1.0 4));         // refinement level 4 (1.0 entry ignored)
    }

    sphere.stl
    {                             // refinement level 5 within 1.0 m
        mode distance;            // refinement level 3 within 2.0 m
        levels ((1.0 5) (2.0 3)); // levels must be ordered nearest first
    }
}

4.4.6 Snapping to surfaces

The next stage of the meshing process involves moving cell vertex points onto surface geometry to remove the jagged castellated surface from the mesh. The process is:

displace the vertices in the castellated boundary onto the STL surface;
solve for relaxation of the internal mesh with the latest displaced boundary vertices;
find the vertices that cause mesh quality parameters to be violated;
reduce the displacement of those vertices from their initial value (at 1) and repeat from 2 until mesh quality is satisfied.

The method uses the settings in the snapControls sub-dictionary in snappyHexMeshDict, listed in Table 4.6.

Keyword	Description	Example

nSmoothPatch	Number of patch smoothing iterations before finding correspondence to surface	3
tolerance	Ratio of distance for points to be attracted by surface feature point or edge, to local maximum edge length	4.0
nSolveIter	Number of mesh displacement relaxation iterations	30
nRelaxIter	Maximum number of snapping relaxation iterations	5
nFeatureSnapIter	Number of feature edge snapping iterations	10
implicitFeatureSnap	Detect (geometric only) features by sampling the surface	false
explicitFeatureSnap	Use castellatedMeshControls features	true
multiRegionFeatureSnap	Detect features between multiple surfaces when using the explicitFeatureSnap	false

Table 4.6: Keywords in the snapControls dictionary of snappyHexMeshDict.

An example is illustrated in the schematic in Figure 4.14 (albeit with mesh motion that looks slightly unrealistic).

$\relax \special {t4ht=$

Figure 4.14: Surface snapping in snappyHexMesh meshing process

4.4.7 Mesh layers

The mesh output from the snapping stage may be suitable for the purpose, although it can produce some irregular cells along boundary surfaces. There is an optional stage of the meshing process which introduces additional layers of hexahedral cells aligned to the boundary surface as illustrated by the dark shaded cells in Figure 4.15.

$\relax \special {t4ht=$

Figure 4.15: Layer addition in snappyHexMesh meshing process

The process of mesh layer addition involves shrinking the existing mesh from the boundary and inserting layers of cells, broadly as follows:

the mesh is projected back from the surface by a specified thickness in the direction normal to the surface;
solve for relaxation of the internal mesh with the latest projected boundary vertices;
check if validation criteria are satisfied otherwise reduce the projected thickness and return to 2; if validation cannot be satisfied for any thickness, do not insert layers;
if the validation criteria can be satisfied, insert mesh layers;
the mesh is checked again; if the checks fail, layers are removed and we return to 2.

The layer addition procedure uses the settings in the addLayersControls sub-dictionary in snappyHexMeshDict; entries are listed in Table 4.7.

Keyword	Description	Example

layers	Dictionary of layers
relativeSizes	Are layer thicknesses relative to undistorted cell size outside layer or absolute?	true/false
expansionRatio	Expansion factor for layer mesh	1.0
finalLayerThickness	Thickness of layer furthest from the wall, either relative or absolute according to the relativeSizes entry	1
firstLayerThickness	Thickness of layer closest to the wall, either relative or absolute according to	0.3
thickness	Overall thickness of all layers	0.3
minThickness	Minimum overall thickness of all layers, below which surface is not extruded	0.1
nGrow	Number of layers of connected faces that are not grown if points are not extruded; helps convergence of layer addition close to features	1
featureAngle	Angle above which surface is not extruded	60
maxFaceThicknessRatio	Face thickness ratio above which surface is not extruded, useful for warped cells	0.5
nSmoothSurfaceNormals	Number of smoothing iterations of surface normals	1
nSmoothThickness	Smooth layer thickness over surface patches	10
minMedialAxisAngle	Angle used to pick up medial axis points	90
maxThicknessToMedialRatio	Reduce layer growth where ratio thickness to medial distance is large	0.3
maxThicknessToMedialRatio	Reduce layer growth where ratio thickness to medial distance is large	0.3
nSmoothNormals	Number of smoothing iterations of interior mesh movement direction	3
nRelaxIter	Maximum number of snapping relaxation iterations	5
nBufferCellsNoExtrude	Create buffer region for new layer terminations	0
nLayerIter	Overall max number of layer addition iterations	50
nRelaxedIter	Max number of iterations after which the controls in the relaxed sub dictionary of meshQuality are used	20

Table 4.7: Keywords in the addLayersControls sub-dictionary of snappyHexMeshDict.

The layers sub-dictionary contains entries for each patch on which the layers are to be applied and the number of surface layers required. The patch name is used because the layers addition relates to the existing mesh, not the surface geometry; hence applied to a patch, not a surface region. An example layers entry is as follows:

layers
{
    sphere.stl_firstSolid
    {
        nSurfaceLayers 1;
    }
    maxY
    {
        nSurfaceLayers 1;
    }
}

Keyword	Description	Example

maxNonOrtho	Maximum non-orthogonality allowed; 180 disables	65
maxBoundarySkewness	Max boundary face skewness allowed; $< \relax \special {t4ht=$ 0 disables	20
maxInternalSkewness	Max internal face skewness allowed; $< \relax \special {t4ht=$ 0 disables	4
maxConcave	Max concaveness allowed; 180 disables	80
minFlatness	Ratio of minimum projected area to actual area; -1 disables	0.5
minVol	Minimum pyramid volume; large negative number, e.g.-1e30 disables	1e-13
minTetQuality	Minimum quality of the tetrahedron formed by the face-centre and variable base point minimum decomposition triangles and the cell centre; set to very negative number, e.g.-1e30 to disable	1e-13
minArea	Minimum face area; $< \relax \special {t4ht=$ 0 disables	-1
minTwist	Minimum face twist; $< \relax \special {t4ht=$ -1 disables	0.05
minDeterminant	Minimum normalised cell determinant; 1 $= \relax \special {t4ht=$ hex; $≤ \relax \special {t4ht=$ 0 illegal cell	0.001
minFaceWeight	0 $→ \relax \special {t4ht=$ 0.5	0.05
minVolRatio	0 $→ \relax \special {t4ht=$ 1.0	0.01
minTriangleTwist	$> \relax \special {t4ht=$ 0 for Fluent compatability	-1
nSmoothScale	Number of error distribution iterations	4
errorReduction	Amount to scale back displacement at error points	0.75
relaxed	Sub-dictionary that can include modified values for the above keyword entries to be used when nRelaxedIter is exceeded in the layer addition process	relaxed { … }